Let  be the set of all calendar dates from 4/30/1789 to 9/25/2014.Let  be the set of names of U.S. presidents.Let  be the set of names of first ladies of the U.S.Consider the following two functions  where  is the name of the president of the U.S. on date  (the incumbent on inauguration days, to avoid ambiguity) and  where  is the name of the first lady of the U.S. during the presidency of president .1. Can the composition  be defined? What about ?2. Which of the following functional inverses exist and which do not? , , ,  

Also remember these comprise what is referred to as the "primary post", i.e., these should be posted in a single post with one response on top of the other. Each should be numbered to clearly show where the response to #1 ends and the response to #2 starts. What is the best type of budget for the law enforcement agency? Why so? What are the strengths and weaknesses of this type of budget? What is more stressful for the police officer – working the street or dealing with the agency administration? Why so? What can be done by the police administrator to reduce this stress felt by officers? Classmate 1 Michael: 1. What is the best type of budget for the law enforcement agency??Why so??What are the strengths and weaknesses of this type of budget?   In a time of increased polarization, misinformation, and civic disillusionment, the budget is the most important document prepared by a local government Morrill, 2021). In the era of community policing and citizen advisory boards, it is evident that the community desires increased involvement, indicated through “defund the police” initiative, politically. New Public Management (NPM) is an emphasis of innovative public services, including internal, external, and citizen participation (Ewens & Van Der Voet, 2019). The interest of participatory governance and increasing government legitimacy is also motivated by the New Public Governance (NPG) agenda (Bartocci., et al., 2019). These efforts are inevitably going to result in Participatory Budgeting as it is politically motivated and incorporates unelected citizens in determining funding priorities and return some political power to the citizens (Bartocci., et al., 2019). I am in support of a hybrid model of this type of budgeting because it places the responsibility on the citizens. There are strengths and weaknesses to this type of budget, but it allows for equity, transparency, trust, and is reflective of community values (Morrill, 2021).   Traditional budgets fail to incorporate the needs of all community members, allowing for bias, inequities, political misconduct, and the lack of transparency and involvement (Morrill, 2021). Under a hybrid Participatory Budgeting concept, the importance for qualified, educated and competent government department leaders is key. Government employees should be of the highest of standards and capabilities in order to address community concerns and needs. Government department leaders would be responsible for identifying budgetary items of importance and provide an annual report itemizing these requests. Government employees, department heads, elected officials, and the public would be involved in the process of participatory innovation (PI) (Ewens & Van Der Voet, 2019). A heavy reliance on the internal capabilities and their expert knowledge in combination with the size and structure of the agency, increases the relevancy of their decision (Ewens & Van Der Voet, 2019). Interagency collaboration and structural innovation from within is what citizens expect from their government and research has shown that the more complex an organizational structure is, (department, divisions, services, etc.) the more likely innovation will be adopted (Ewens & Van Der Voet, 2019). This essentially means that the more experts there are, the more informed the ideas are, and the greater the ability to offer support for those ideas. This is essential to provide citizens with budgetary items and justification for the needs. In doing so, convincing citizens and getting the “buy in” and support is the goal. Citizens should weigh in on the budget and provide guidance in modifying or reallocating funds based on the needs of the community. This not only provides transparency and gives an active role to citizens, it transfers responsibility to the public for the decisions made. Hearings and or committees could satisfy the citizen’s role in the innovation process, or even providing public surveys on particular budgetary items. These participatory practices would incorporate elected officials, managers/department leaders, community foundations, and non-profit organizations for maximized information and innovation (Bartocci., et al., 2019). Once a line-item type budget proposal is established the items would be discussed, agreed upon, and approved by the board of alderman.   This would inherently have weaknesses, especially in police budgeting, due to political climates. Police services are localized and accomplish many goals including social services such as, drug treatment, mental health, and homelessness (Beck & Goldstein, 2018).  In policing it has been shown that a decrease in crime is associated with increased police spending and decrease in social services; as police effectively accomplish both of these goals (Beck & Goldstein, 2018). Despite the facts, citizens are swayed by personal bias and political influence and would naturally be against funding policing initiatives. Increasing social services in combination with the influx of illegal immigration, goes against the effectiveness of law enforcement addressing social problems and decreasing crime (Beck & Goldstein, 2018). This would negatively impact society, but would give citizens the opportunity to “make their bed and lay in it”. Any type of budget has strengths and weaknesses. Maximizing innovation and collaboration in the decision making process will ensure equity, inclusiveness, and transparency. Holding politicians accountable to represent the community, I think is the most appropriate for our culture of today.   2. What is more stressful for the police officer – working the street or dealing with the agency administration??Why so??What can be done by the police administrator to reduce this stress felt by officers?   Dealing with the agencies administration has a greater impact on officer stress than working the street. This is for many reasons, often related to managerial incompetence, ineffectiveness, and lack of leadership which affects their officers’ psychological health, work attitude, and jobs performance (Houdmont, et al., 2020). Analysis shows that work related conditions contribute to higher levels of stress affecting work product, family, and social life (Queiros, Et al., 2020). The nature of the job is inherently dangerous and many outside factors play into an officer’s stress. Officers have operational factors (patrol, community services, and crime prevention responsibilities), as well as organizational tasks (policies/procedures, administrative duties, and public information responsibilities) that they are responsible for (Acquadro, et al., 2018). It is the duty of leadership in the police administration to recognize, identify, and rectify many of the roots related to stress, even if it is not directly work related.  Police suffer from many physical and mental health disorders and diseases induced by stress, including cardiovascular disease, sleep disorders, obesity, anxiety, depression, Post Traumatic Stress Disorder (PTSD), stress related injuries, and many others (Acquadro, et al., 2018). These facts make it imperative that leadership are competent and receive training and skill development in addressing the signs, symptoms, and mechanisms to address stress at work (Houdmont, et al., 2020). Many stresses stem from outside elements that “spill over” into the workplace. Martial problems, political climate, media, and lack of social support from family and society are stress contributors, but becomes an administrations problem because they are tasked with mitigating stress (Queiros, Et al., 2020). The importance of stress intervention is paramount because it leads to hypervigilance, negative interactions with citizens, cynicism, propensity to use excessive force, depression, and even suicide (Queiros, Et al., 2020).  Administrations need to respond to officers’ stress with urgency and purpose. Providing paid health and mental health care is something I have always been a proponent of. Officers dedicate their lives to the community, the least the community can do is cover the benefit costs to provide health and mental health care. Influences on officer’s wellbeing, quality of life, job performance, families, and citizens of society as a whole would benefit from routine health and mental health checkups, free of cost (Queiros, Et al., 2020). Policies requiring yearly health checkups and optional mental health services such as the Employee Assistance Program (EAP) or Crisis Intervention and Stress Management (CISM) programs have proven effective to manage stress (Acquadro, et al., 2018). This in combination with yearly Physical Testing standards and encouraged physical fitness is also beneficial for stress management. In-service training should implement training and stress management to include physical fitness, diet, mental health, meditation, and information about maladaptive or negative (alcohol/drug abuse, domestic abuse, isolation, etc.) and adaptive or positive coping strategies (humor, working out, hobby, etc. ) (Acquadro, et al., 2018). Supervisory responsibility can play a part in mitigating stress as well. Supervisors could offer paid time to exercise or decompress. Building on-site fitness centers and/or partnerships with fitness clubs is a positive initiative as well. Encouraging officers to eat healthy and pack their lunch is helpful advice, as well as offer emotional support and encouragement. Supervisors can ensure officers are able to take off from work and even encourage it in some cases. Supervisors not only have to take proactive steps to address stress and work performance issues through accountability, they need to be able to relate to officers and understand the cause of the issue. Administrators and supervisors collectively can minimize stress through training, competence, accountability, and compassion. Allowing officers time off and making accommodations to solve root issues not only prevents work-related problems, but also builds the relationship between officers and their superiors. Police administration requires and adaptive response to the contemporary challenges and effective leadership to decrease stress and improve the quality of life and wellbeing of officers (Queiros, Et al., 2020) (Acquadro, et al., 2018). Administrators must be knowledgeable, dedicated, and respected to accomplish the ultimate goal of quality leadership.  References  Acquadro Maran, D., Zedda, M., & Varetto, A. (2018). Physical Practice and Wellness Courses Reduce Distress and Improve Wellbeing In Police Officers. International Journal of Environmental Research and Public Health, 15(4), 578–. https://doi.org/10.3390/ijerph15040578  Bartocci, L., Grossi, G., & Mauro, S. G. (2019). Towards A hybrid Logic Of Participatory Budgeting. The International Journal Of Public Sector Management, 32(1), 65–79. https://doi.org/10.1108/IJPSM-06-2017-0169  Beck, B., & Goldstein, A. (2018). Governing Through Police? Housing Market Reliance, Welfare Retrenchment, And Police Budgeting In An Era Of Declining Crime. Social Forces, 96(3), 1183–1210. https://doi.org/10.1093/sf/sox076  Ewens, H., & Van Der Voet, J. (2019). Organizational Complexity and Participatory Innovation: Participatory Budgeting In Local Government. Public Management Review, 21(12), 1848–1866. https://doi.org/10.1080/14719037.2019.1577908  Houdmont, J., Jachens, L., Randall, R., Colwell, J., & Gardner, S. (2020). Stress Management Competency Framework in English policing. Occupational Medicine (Oxford), 70(1), 31–37. https://doi.org/10.1093/occmed/kqz143  Morrill, C. (2021). To Increase Trust in Government, Reinvent the Local Government Budget. State & Local Government Review, 53(1), 10–13. https://doi.org/10.1177/0160323X211000835  Queirós, C., Passos, F., Bártolo, A., Marques, A., D Silva, C. F., & Pereira, A. (2020). Burnout and Stress Measurement in Police Officers: Literature Review and a Study With the Operational Police Stress Questionnaire. Frontiers in Psychology, 11, 587–587. https://doi.org/10.3389/fpsyg.2020.00587  Classmate 2 Robert:  What is the best type of budget for the law enforcement agency? Why so? What are the strengths and weaknesses of this type of budget? There are different types of budgets that law enforcement agencies use. Two of them are Line-Item and Zero-Based Budgets (Stuart, n.d.) My agency uses the Line-Item Budget where the President of the college determines amounts allocated to all departments. Within my department or cost-center, my budget is spread across large categories or lines that represent recurring expenses. Our biggest expenditure for my department is salary and the rest of the expenditures are spread across smaller general categories: training, travel, uniforms and recurring software licensing. The main disadvantage to this method is, as a department head, I do not have input into the amounts that are allocated to the lines or adjust amounts to lines or categories that that need special emphasis this year. Another disadvantage is the approach assumes all expenses are recurring at the same rate and do not adjust to meet special expenditures. Any special purpose or large item requires preparing a proposal for adding a line item, getting approval, and selecting a vetted vender to provide that item or service.  Some advantages to the line-item budget are the budget is pushed down from the administration to the department, does not require extensive preparation at department level, and permits some flexibility to move money between line items at the department level that does not require approval from the administration (Stuart, n.d.) The Zero-based budget begins with each agency reviewing each item and determining if the items are still needed. Each item is reviewed and must be justified to receive the funds (Stuart,  n.d.). The advantage to this type of budget gives law enforcement leaders the ability to shape expenditures along desired operational lines by emphasizing one item over another for the current fiscal year and adjusting that emphasis to another priority the following year. For instance, if the department is due to replace vehicles this year, the leader can establish internal priorities among budget items to purchase the vehicles this year. By placing emphasis on one item now, the leader can project which items can be adjusted for the next budget cycle to support the strategic goals of the department (Orrick, n.d.)   As a law enforcement administrator, I prefer the Zero-based budget for the flexibility to emphasize budget items based on the goals of the department yet meet the fiscal limitations established by the college’s administration. Likewise, as justification is prepared for the budget items, I could inform the administration about the rationale for selecting them items, why they are prioritized and the potential risks for not approving items. As the law enforcement leader, providing this information gives the administration the awareness of the issues and liabilities.   Also, training and equipment can be placed on a rotational basis to support maintaining an operational vehicle fleet and supporting the professional development of officers. Our agency does not have a large vehicle fleet so the expense of purchasing new vehicles does not occur on a regular basis. However, purchasing other uniform equipment and training equipment and certifications occurs more frequently but at a smaller scale than purchasing vehicles so budget amounts can fluctuate to meet those requirements.  Orrick, W. (n.d.).  Best Practices Guide for Budgeting in Small Police Agencies. Retrieved from  https://www.theiacp.org/sites/default/files/2018-0... Stuart, R.  (n.d.).  Budgeting Basics. Retrieved from  http://www.icje.org/articles/Budgeting Basics.pdf 2.  What is more stressful for the police officer – working the street or dealing with the agency administration? Why so? What can be done by the police administrator to reduce this stress felt by officers? For most patrol officers, dealing with stressors in the street are easier than dealing with the organizational stressors caused by the administration (Randall and Buys, 2013). Officers who have several years of experience on the streets are tuned into that environment and know how to deal with people, the types of calls they will encounter and are accustomed to the operational stressors of patrol duties (Randall and Buys, 2013). Not only are they attuned to that environment daily, but can read their shift partner’s reactions, tone of voice, body language and have a familiarity with the people in their assigned area. Picking up on your partner’s non-verbal cues are a necessity when working on the streets and  this becomes second nature and is an essential part of officer safety. That familiarity with those operational stressors provides a degree of stability to the patrol officer. By working with other officers in that environment they forge working relationships and trust among the officers who are united by their job.   Most officers have different levels of comfort when dealing with the administration and, in some instances, they would choose to avoid dealing with senior leaders. Leaders need to be aware of officers tentativeness and reluctance to speak freely when asked questions. This can be due to a lack of trust in the administration by the officers. This lack of trust can be characterized as an  organizational stressor brought on by an actual or perceived non-supportive work environment (Randall and Buys, 2013). Leaders can directly influence this stressor by changing the culture of the department through transparent accountability across the ranks, stating a clear vision, and encouraging open communication.  Other types of stressors that influence officers are external and personal stressors (Oliver and Meier, 2009).  Today, external stressors seem to be increasing as law enforcement use of force incidents are dissected in social media.  Officers, concerned about job security, criminal and civil liability, and amount of scrutiny they may receive because of a use of force incident, will feel these stressors as well. The officers’ perception of a lack of support from administration will add to this stressor. Leaders should attempt to remove some of this stress by promoting a work environment that openly communicates expectations, provides recognition of those who do good work and hold officers accountable to department standards regardless of rank.   Personal stressors are a leadership and an individual responsibility. Investing in officers to help improve their personal stressors without considering the work climate will have little success (Randall and Buys, 2013).  The leader should create a supportive environment that encourages officers to discuss traumatic experiences both on and off the job with professionals. Since the personal stressors can be family, health, financial or mental issues, leadership should be attentive to warning signals peers, supervisors, or other indicators the officer is having personal issues. Typically, officers that seek professional help choose to do so outside of department provided services (Fleischmann, M, Strode, P, Broussard, B and Compton, M, 2018). That suggests that officers are unwilling to seek professional assistance from the department and may be suspicious of those service providers. Therefore, this becomes a leadership issue. The leader can influence the climate of the department to encourage using those resources to help deal with behavioral issues before those behaviors become a significant liability.        Menard K & Arter M., (2013) Police officer alcohol use and trauma symptoms: Associations with critical incidents, coping, and social stressors. Retrieved from https://www-proquest-com.ezproxy1.apus.edu/docview/1272643592/fulltextPDF/864767BF6FBA4FC8PQ/1?accountid=8289 Oliver, W & Meier, C (2009). Considering the efficacy of stress management education on small-town and rural police. Retrieved from  http://ezproxy.apus.edu/login?url=http://search. ebscohost.com/login.aspx?direct =true&db=i3h&AN=37291342&site=ehost-live&scope=site Fleischmann, M, Strode, P, Broussard, B & Compton, M. (2018) Law enforcement officers’ perceptions of and responses to traumatic events: a survey of officers completing Crisis Intervention Team training. Retrieved from https://web-a-ebscohost-com.ezproxy1.apus.edu/ ehost/pdfviewer/pdfviewer?vid=1&sid=e2b29727-1c0c-4740-a279-894c9e2217d4%40sdc-v-sessmgr01 Classmate 3 Hannah: 1. What is the best type of budget for the law enforcement agency? Why so? What are the strengths and weaknesses of this type of budget? Lauded by the United Nations as a "best practice of local democracy," Participatory Budgeting (PB) enables the stakeholders within a local community to determine what and to what degree a proposed action is funded (Lerner, 2011). The concept of Participatory Budgeting was first applied in Brazil in 1989, and has gained international attention and implementation within such communities (Hagelskamp et al, 2020). The priorities of the stakeholder take precedent in contrast with a more traditional, legislative-based budget, and the purported advantages of PB have been touted as numerous. Lerner (2011) describes how PB is a superior system in that it promotes: democracy, in that the people vote on the proposals; community, as members build a greater sense of ownership by having a direct impact on their neighborhood's priorities; transparency, given the fact that the locals are made aware of and have a direct say in the appropriation of funds; education, as the public become more aware of how the democratic political system works as well as the subjects that are of importance within a more diverse community; efficiency, in that there is less opportunity for "pork" or similar expenditures; and social justice, as every member is allotted one vote, and so no voice is granted more value than that of the next. Although Chicago implemented PB in 2011 and New York City in 2013, there is still not enough data nor studies to support that PB is definitively a more equitable budgeting system (Hagelskamp et al, 2020), as it is too soon for such an analysis. Still, given the results from Brazil, the support of the United Nations and the World Bank (Lerner, 2011), and the potential for a process that involves the community that these budgets are both derived from and effect, a Participatory Budgeting system is most advantageous. Hagelskamp, C., Silliman, R., Godfrey, E., & Schleifer, D. (2020). Shifting Priorities: Participatory Budgeting in New York City is Associated with Increased Investments in Schools, Street and Traffic Improvements, and Public Housing. New Political Science, 42(2), 171-196. Lerner, J. (2011). Participatory budgeting: Building community agreement around tough budget decisions. National Civic Review, 100(2), 30-35. 2. What is more stressful for the police officer – working the street or dealing with the agency administration? Why so? What can be done by the police administrator to reduce this stress felt by officers? The stress related to working on the street pales in comparison to interacting with a police agency administration, as has been indicated by a study of police stressors by Anderson, Litzenberger, and Plecas (2002). Many of these stressors are described as resulting from "factors within the organization and organizational structure that... [result in a] lack of administrative support, the promotion process, inadequate training or equipment, excessive paperwork, intra-departmental politics, and frustrations with the criminal justice system and court leniency," (Anderson et al, p. 403). The question of how an agency's administration can be the root of such stress when a law enforcement officer is faced with the constant stress that is part of the nature of the job (responding to domestic cases, having to rectify disputes, the potential for violent altercations, etc) is answered by the overall feeling of lacking support. A law enforcement officer would still be in need of resources, mental health or otherwise, after responding to a traumatic call, but to respond to that call with the perception that the officer's supervisor and administration may not support them exacerbates an already stressful situation. Purba and Demou found that organizational stressors related to police work are derived from an officer's feeling that many of the hurdles that the administration puts in place are "oppressive, unnecessary, unavoidable, and uncontrollable," (2019). One of the easiest methods (theoretically) of alleviating this source of stress would be to change or modify restrictive or oppressive policies to promote a culture of trust and cohesion. Moreover, training police leaders on how to detect and intervene when one of their subordinates is negatively effected by a stressor brought on by organizational challenges could also turn the tide (Purba & Demou, 2019). Anderson, G., Litzenberger, & Plecas, D. (2002). Physical evidence of police officer stress. Policing: an international journal of police strategies & management. Purba, A., & Demou, E. (2019). The relationship between organisational stressors and mental wellbeing within police officers: a systematic review. BMC public health, 19(1), 1-21.

Due 07/22/19 by 2PM EST Post a blog post that includes: An explanation of the individual, family, and group context in your field education experience Reference Birkenmaier, J., & Berg-Weger, M. (2018). The practicum companion for social work: Integrating class and fieldwork (4th ed.). New York, NY: Pearson. Chapter 6, “Social Work Practice in the Field: Working with Individuals and Families” (pp. 117-154)Chapter 7, “Social Work Practice in the Field: Working with Groups” (pp. 156-185)